Polytope of Type {15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {15,4}
Number of vertices, edges, etc : 240, 480, 64
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15,4}*960
3-fold quotients : {5,4}*640
4-fold quotients : {15,4}*480
6-fold quotients : {5,4}*320
12-fold quotients : {5,4}*160
32-fold quotients : {15,2}*60
96-fold quotients : {5,2}*20
160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)( 42,137)
( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)( 50,155)
( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)( 58,147)
( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)( 66, 98)
( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)( 74,105)
( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)( 82,123)
( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)( 90,115)
( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)(162,322)
(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)(170,329)
(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)(178,347)
(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)(186,339)
(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)(194,450)
(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)(202,457)
(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)(210,475)
(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)(218,467)
(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)(226,418)
(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)(234,425)
(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)(242,443)
(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)(250,435)
(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)(258,386)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)(266,393)
(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)(274,411)
(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)(282,403)
(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)(290,354)
(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)(298,361)
(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)(306,379)
(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)(314,371)
(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)(483,484)
(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)(500,506)
(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)(516,611)
(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)(524,620)
(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)(532,634)
(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)(540,626)
(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)(548,579)
(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)(556,588)
(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)(564,602)
(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)(572,594)
(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)(644,803)
(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)(652,812)
(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)(660,826)
(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)(668,818)
(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)(676,931)
(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)(684,940)
(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)(692,954)
(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)(700,946)
(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)(708,899)
(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)(716,908)
(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)(724,922)
(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)(732,914)
(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)(740,867)
(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)(748,876)
(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)(756,890)
(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)(764,882)
(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)(772,835)
(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)(780,844)
(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)(788,858)
(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)(796,850)
(797,854)(798,853)(799,856)(800,855);;
s1 := ( 1,193)( 2,194)( 3,224)( 4,223)( 5,204)( 6,203)( 7,213)( 8,214)
( 9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)( 32,195)
( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)( 40,182)
( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)( 48,175)
( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)( 64,163)
( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)( 72,310)
( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)( 80,303)
( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)( 96,291)
( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)(104,278)
(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)(112,271)
(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)(120,281)
(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)(128,259)
(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)(136,246)
(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)(144,239)
(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)(152,249)
(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)(160,227)
(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)(328,374)
(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)(336,367)
(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)(344,377)
(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)(352,355)
(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)(392,470)
(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)(400,463)
(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)(408,473)
(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)(416,451)
(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)(426,443)
(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,674)(482,673)
(483,703)(484,704)(485,683)(486,684)(487,694)(488,693)(489,699)(490,700)
(491,677)(492,678)(493,689)(494,690)(495,687)(496,688)(497,685)(498,686)
(499,692)(500,691)(501,680)(502,679)(503,697)(504,698)(505,695)(506,696)
(507,681)(508,682)(509,701)(510,702)(511,675)(512,676)(513,642)(514,641)
(515,671)(516,672)(517,651)(518,652)(519,662)(520,661)(521,667)(522,668)
(523,645)(524,646)(525,657)(526,658)(527,655)(528,656)(529,653)(530,654)
(531,660)(532,659)(533,648)(534,647)(535,665)(536,666)(537,663)(538,664)
(539,649)(540,650)(541,669)(542,670)(543,643)(544,644)(545,770)(546,769)
(547,799)(548,800)(549,779)(550,780)(551,790)(552,789)(553,795)(554,796)
(555,773)(556,774)(557,785)(558,786)(559,783)(560,784)(561,781)(562,782)
(563,788)(564,787)(565,776)(566,775)(567,793)(568,794)(569,791)(570,792)
(571,777)(572,778)(573,797)(574,798)(575,771)(576,772)(577,738)(578,737)
(579,767)(580,768)(581,747)(582,748)(583,758)(584,757)(585,763)(586,764)
(587,741)(588,742)(589,753)(590,754)(591,751)(592,752)(593,749)(594,750)
(595,756)(596,755)(597,744)(598,743)(599,761)(600,762)(601,759)(602,760)
(603,745)(604,746)(605,765)(606,766)(607,739)(608,740)(609,706)(610,705)
(611,735)(612,736)(613,715)(614,716)(615,726)(616,725)(617,731)(618,732)
(619,709)(620,710)(621,721)(622,722)(623,719)(624,720)(625,717)(626,718)
(627,724)(628,723)(629,712)(630,711)(631,729)(632,730)(633,727)(634,728)
(635,713)(636,714)(637,733)(638,734)(639,707)(640,708)(801,834)(802,833)
(803,863)(804,864)(805,843)(806,844)(807,854)(808,853)(809,859)(810,860)
(811,837)(812,838)(813,849)(814,850)(815,847)(816,848)(817,845)(818,846)
(819,852)(820,851)(821,840)(822,839)(823,857)(824,858)(825,855)(826,856)
(827,841)(828,842)(829,861)(830,862)(831,835)(832,836)(865,930)(866,929)
(867,959)(868,960)(869,939)(870,940)(871,950)(872,949)(873,955)(874,956)
(875,933)(876,934)(877,945)(878,946)(879,943)(880,944)(881,941)(882,942)
(883,948)(884,947)(885,936)(886,935)(887,953)(888,954)(889,951)(890,952)
(891,937)(892,938)(893,957)(894,958)(895,931)(896,932)(897,898)(899,927)
(900,928)(901,907)(902,908)(903,918)(904,917)(905,923)(906,924)(909,913)
(910,914)(915,916)(919,921)(920,922);;
s2 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,494)( 6,493)( 7,496)( 8,495)
( 9,482)( 10,481)( 11,484)( 12,483)( 13,485)( 14,486)( 15,487)( 16,488)
( 17,505)( 18,506)( 19,507)( 20,508)( 21,510)( 22,509)( 23,512)( 24,511)
( 25,498)( 26,497)( 27,500)( 28,499)( 29,501)( 30,502)( 31,503)( 32,504)
( 33,521)( 34,522)( 35,523)( 36,524)( 37,526)( 38,525)( 39,528)( 40,527)
( 41,514)( 42,513)( 43,516)( 44,515)( 45,517)( 46,518)( 47,519)( 48,520)
( 49,537)( 50,538)( 51,539)( 52,540)( 53,542)( 54,541)( 55,544)( 56,543)
( 57,530)( 58,529)( 59,532)( 60,531)( 61,533)( 62,534)( 63,535)( 64,536)
( 65,553)( 66,554)( 67,555)( 68,556)( 69,558)( 70,557)( 71,560)( 72,559)
( 73,546)( 74,545)( 75,548)( 76,547)( 77,549)( 78,550)( 79,551)( 80,552)
( 81,569)( 82,570)( 83,571)( 84,572)( 85,574)( 86,573)( 87,576)( 88,575)
( 89,562)( 90,561)( 91,564)( 92,563)( 93,565)( 94,566)( 95,567)( 96,568)
( 97,585)( 98,586)( 99,587)(100,588)(101,590)(102,589)(103,592)(104,591)
(105,578)(106,577)(107,580)(108,579)(109,581)(110,582)(111,583)(112,584)
(113,601)(114,602)(115,603)(116,604)(117,606)(118,605)(119,608)(120,607)
(121,594)(122,593)(123,596)(124,595)(125,597)(126,598)(127,599)(128,600)
(129,617)(130,618)(131,619)(132,620)(133,622)(134,621)(135,624)(136,623)
(137,610)(138,609)(139,612)(140,611)(141,613)(142,614)(143,615)(144,616)
(145,633)(146,634)(147,635)(148,636)(149,638)(150,637)(151,640)(152,639)
(153,626)(154,625)(155,628)(156,627)(157,629)(158,630)(159,631)(160,632)
(161,649)(162,650)(163,651)(164,652)(165,654)(166,653)(167,656)(168,655)
(169,642)(170,641)(171,644)(172,643)(173,645)(174,646)(175,647)(176,648)
(177,665)(178,666)(179,667)(180,668)(181,670)(182,669)(183,672)(184,671)
(185,658)(186,657)(187,660)(188,659)(189,661)(190,662)(191,663)(192,664)
(193,681)(194,682)(195,683)(196,684)(197,686)(198,685)(199,688)(200,687)
(201,674)(202,673)(203,676)(204,675)(205,677)(206,678)(207,679)(208,680)
(209,697)(210,698)(211,699)(212,700)(213,702)(214,701)(215,704)(216,703)
(217,690)(218,689)(219,692)(220,691)(221,693)(222,694)(223,695)(224,696)
(225,713)(226,714)(227,715)(228,716)(229,718)(230,717)(231,720)(232,719)
(233,706)(234,705)(235,708)(236,707)(237,709)(238,710)(239,711)(240,712)
(241,729)(242,730)(243,731)(244,732)(245,734)(246,733)(247,736)(248,735)
(249,722)(250,721)(251,724)(252,723)(253,725)(254,726)(255,727)(256,728)
(257,745)(258,746)(259,747)(260,748)(261,750)(262,749)(263,752)(264,751)
(265,738)(266,737)(267,740)(268,739)(269,741)(270,742)(271,743)(272,744)
(273,761)(274,762)(275,763)(276,764)(277,766)(278,765)(279,768)(280,767)
(281,754)(282,753)(283,756)(284,755)(285,757)(286,758)(287,759)(288,760)
(289,777)(290,778)(291,779)(292,780)(293,782)(294,781)(295,784)(296,783)
(297,770)(298,769)(299,772)(300,771)(301,773)(302,774)(303,775)(304,776)
(305,793)(306,794)(307,795)(308,796)(309,798)(310,797)(311,800)(312,799)
(313,786)(314,785)(315,788)(316,787)(317,789)(318,790)(319,791)(320,792)
(321,809)(322,810)(323,811)(324,812)(325,814)(326,813)(327,816)(328,815)
(329,802)(330,801)(331,804)(332,803)(333,805)(334,806)(335,807)(336,808)
(337,825)(338,826)(339,827)(340,828)(341,830)(342,829)(343,832)(344,831)
(345,818)(346,817)(347,820)(348,819)(349,821)(350,822)(351,823)(352,824)
(353,841)(354,842)(355,843)(356,844)(357,846)(358,845)(359,848)(360,847)
(361,834)(362,833)(363,836)(364,835)(365,837)(366,838)(367,839)(368,840)
(369,857)(370,858)(371,859)(372,860)(373,862)(374,861)(375,864)(376,863)
(377,850)(378,849)(379,852)(380,851)(381,853)(382,854)(383,855)(384,856)
(385,873)(386,874)(387,875)(388,876)(389,878)(390,877)(391,880)(392,879)
(393,866)(394,865)(395,868)(396,867)(397,869)(398,870)(399,871)(400,872)
(401,889)(402,890)(403,891)(404,892)(405,894)(406,893)(407,896)(408,895)
(409,882)(410,881)(411,884)(412,883)(413,885)(414,886)(415,887)(416,888)
(417,905)(418,906)(419,907)(420,908)(421,910)(422,909)(423,912)(424,911)
(425,898)(426,897)(427,900)(428,899)(429,901)(430,902)(431,903)(432,904)
(433,921)(434,922)(435,923)(436,924)(437,926)(438,925)(439,928)(440,927)
(441,914)(442,913)(443,916)(444,915)(445,917)(446,918)(447,919)(448,920)
(449,937)(450,938)(451,939)(452,940)(453,942)(454,941)(455,944)(456,943)
(457,930)(458,929)(459,932)(460,931)(461,933)(462,934)(463,935)(464,936)
(465,953)(466,954)(467,955)(468,956)(469,958)(470,957)(471,960)(472,959)
(473,946)(474,945)(475,948)(476,947)(477,949)(478,950)(479,951)(480,952);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)
( 42,137)( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)
( 50,155)( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)
( 58,147)( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)
( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)
( 74,105)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)
( 82,123)( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)
( 90,115)( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)
(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)
(170,329)(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)
(178,347)(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)
(186,339)(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)
(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)
(202,457)(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)
(210,475)(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)
(218,467)(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)
(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)
(234,425)(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)
(242,443)(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)
(250,435)(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)
(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)
(266,393)(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)
(274,411)(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)
(282,403)(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)
(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)
(298,361)(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)
(306,379)(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)
(314,371)(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)
(483,484)(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)
(500,506)(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)
(516,611)(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)
(524,620)(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)
(532,634)(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)
(540,626)(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)
(548,579)(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)
(556,588)(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)
(564,602)(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)
(572,594)(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)
(644,803)(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)
(652,812)(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)
(660,826)(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)
(668,818)(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)
(676,931)(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)
(684,940)(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)
(692,954)(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)
(700,946)(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)
(708,899)(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)
(716,908)(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)
(724,922)(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)
(732,914)(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)
(740,867)(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)
(748,876)(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)
(756,890)(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)
(764,882)(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)
(772,835)(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)
(780,844)(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)
(788,858)(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)
(796,850)(797,854)(798,853)(799,856)(800,855);
s1 := Sym(960)!( 1,193)( 2,194)( 3,224)( 4,223)( 5,204)( 6,203)( 7,213)
( 8,214)( 9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)
( 24,217)( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)
( 32,195)( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)
( 40,182)( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)
( 48,175)( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)
( 64,163)( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)
( 72,310)( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)
( 80,303)( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)
( 96,291)( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)
(104,278)(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)
(112,271)(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)
(120,281)(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)
(128,259)(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)
(136,246)(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)
(144,239)(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)
(152,249)(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)
(160,227)(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)
(328,374)(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)
(336,367)(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)
(344,377)(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)
(352,355)(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)
(392,470)(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)
(400,463)(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)
(408,473)(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)
(416,451)(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)
(426,443)(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,674)
(482,673)(483,703)(484,704)(485,683)(486,684)(487,694)(488,693)(489,699)
(490,700)(491,677)(492,678)(493,689)(494,690)(495,687)(496,688)(497,685)
(498,686)(499,692)(500,691)(501,680)(502,679)(503,697)(504,698)(505,695)
(506,696)(507,681)(508,682)(509,701)(510,702)(511,675)(512,676)(513,642)
(514,641)(515,671)(516,672)(517,651)(518,652)(519,662)(520,661)(521,667)
(522,668)(523,645)(524,646)(525,657)(526,658)(527,655)(528,656)(529,653)
(530,654)(531,660)(532,659)(533,648)(534,647)(535,665)(536,666)(537,663)
(538,664)(539,649)(540,650)(541,669)(542,670)(543,643)(544,644)(545,770)
(546,769)(547,799)(548,800)(549,779)(550,780)(551,790)(552,789)(553,795)
(554,796)(555,773)(556,774)(557,785)(558,786)(559,783)(560,784)(561,781)
(562,782)(563,788)(564,787)(565,776)(566,775)(567,793)(568,794)(569,791)
(570,792)(571,777)(572,778)(573,797)(574,798)(575,771)(576,772)(577,738)
(578,737)(579,767)(580,768)(581,747)(582,748)(583,758)(584,757)(585,763)
(586,764)(587,741)(588,742)(589,753)(590,754)(591,751)(592,752)(593,749)
(594,750)(595,756)(596,755)(597,744)(598,743)(599,761)(600,762)(601,759)
(602,760)(603,745)(604,746)(605,765)(606,766)(607,739)(608,740)(609,706)
(610,705)(611,735)(612,736)(613,715)(614,716)(615,726)(616,725)(617,731)
(618,732)(619,709)(620,710)(621,721)(622,722)(623,719)(624,720)(625,717)
(626,718)(627,724)(628,723)(629,712)(630,711)(631,729)(632,730)(633,727)
(634,728)(635,713)(636,714)(637,733)(638,734)(639,707)(640,708)(801,834)
(802,833)(803,863)(804,864)(805,843)(806,844)(807,854)(808,853)(809,859)
(810,860)(811,837)(812,838)(813,849)(814,850)(815,847)(816,848)(817,845)
(818,846)(819,852)(820,851)(821,840)(822,839)(823,857)(824,858)(825,855)
(826,856)(827,841)(828,842)(829,861)(830,862)(831,835)(832,836)(865,930)
(866,929)(867,959)(868,960)(869,939)(870,940)(871,950)(872,949)(873,955)
(874,956)(875,933)(876,934)(877,945)(878,946)(879,943)(880,944)(881,941)
(882,942)(883,948)(884,947)(885,936)(886,935)(887,953)(888,954)(889,951)
(890,952)(891,937)(892,938)(893,957)(894,958)(895,931)(896,932)(897,898)
(899,927)(900,928)(901,907)(902,908)(903,918)(904,917)(905,923)(906,924)
(909,913)(910,914)(915,916)(919,921)(920,922);
s2 := Sym(960)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,494)( 6,493)( 7,496)
( 8,495)( 9,482)( 10,481)( 11,484)( 12,483)( 13,485)( 14,486)( 15,487)
( 16,488)( 17,505)( 18,506)( 19,507)( 20,508)( 21,510)( 22,509)( 23,512)
( 24,511)( 25,498)( 26,497)( 27,500)( 28,499)( 29,501)( 30,502)( 31,503)
( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,526)( 38,525)( 39,528)
( 40,527)( 41,514)( 42,513)( 43,516)( 44,515)( 45,517)( 46,518)( 47,519)
( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,542)( 54,541)( 55,544)
( 56,543)( 57,530)( 58,529)( 59,532)( 60,531)( 61,533)( 62,534)( 63,535)
( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,558)( 70,557)( 71,560)
( 72,559)( 73,546)( 74,545)( 75,548)( 76,547)( 77,549)( 78,550)( 79,551)
( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,574)( 86,573)( 87,576)
( 88,575)( 89,562)( 90,561)( 91,564)( 92,563)( 93,565)( 94,566)( 95,567)
( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,590)(102,589)(103,592)
(104,591)(105,578)(106,577)(107,580)(108,579)(109,581)(110,582)(111,583)
(112,584)(113,601)(114,602)(115,603)(116,604)(117,606)(118,605)(119,608)
(120,607)(121,594)(122,593)(123,596)(124,595)(125,597)(126,598)(127,599)
(128,600)(129,617)(130,618)(131,619)(132,620)(133,622)(134,621)(135,624)
(136,623)(137,610)(138,609)(139,612)(140,611)(141,613)(142,614)(143,615)
(144,616)(145,633)(146,634)(147,635)(148,636)(149,638)(150,637)(151,640)
(152,639)(153,626)(154,625)(155,628)(156,627)(157,629)(158,630)(159,631)
(160,632)(161,649)(162,650)(163,651)(164,652)(165,654)(166,653)(167,656)
(168,655)(169,642)(170,641)(171,644)(172,643)(173,645)(174,646)(175,647)
(176,648)(177,665)(178,666)(179,667)(180,668)(181,670)(182,669)(183,672)
(184,671)(185,658)(186,657)(187,660)(188,659)(189,661)(190,662)(191,663)
(192,664)(193,681)(194,682)(195,683)(196,684)(197,686)(198,685)(199,688)
(200,687)(201,674)(202,673)(203,676)(204,675)(205,677)(206,678)(207,679)
(208,680)(209,697)(210,698)(211,699)(212,700)(213,702)(214,701)(215,704)
(216,703)(217,690)(218,689)(219,692)(220,691)(221,693)(222,694)(223,695)
(224,696)(225,713)(226,714)(227,715)(228,716)(229,718)(230,717)(231,720)
(232,719)(233,706)(234,705)(235,708)(236,707)(237,709)(238,710)(239,711)
(240,712)(241,729)(242,730)(243,731)(244,732)(245,734)(246,733)(247,736)
(248,735)(249,722)(250,721)(251,724)(252,723)(253,725)(254,726)(255,727)
(256,728)(257,745)(258,746)(259,747)(260,748)(261,750)(262,749)(263,752)
(264,751)(265,738)(266,737)(267,740)(268,739)(269,741)(270,742)(271,743)
(272,744)(273,761)(274,762)(275,763)(276,764)(277,766)(278,765)(279,768)
(280,767)(281,754)(282,753)(283,756)(284,755)(285,757)(286,758)(287,759)
(288,760)(289,777)(290,778)(291,779)(292,780)(293,782)(294,781)(295,784)
(296,783)(297,770)(298,769)(299,772)(300,771)(301,773)(302,774)(303,775)
(304,776)(305,793)(306,794)(307,795)(308,796)(309,798)(310,797)(311,800)
(312,799)(313,786)(314,785)(315,788)(316,787)(317,789)(318,790)(319,791)
(320,792)(321,809)(322,810)(323,811)(324,812)(325,814)(326,813)(327,816)
(328,815)(329,802)(330,801)(331,804)(332,803)(333,805)(334,806)(335,807)
(336,808)(337,825)(338,826)(339,827)(340,828)(341,830)(342,829)(343,832)
(344,831)(345,818)(346,817)(347,820)(348,819)(349,821)(350,822)(351,823)
(352,824)(353,841)(354,842)(355,843)(356,844)(357,846)(358,845)(359,848)
(360,847)(361,834)(362,833)(363,836)(364,835)(365,837)(366,838)(367,839)
(368,840)(369,857)(370,858)(371,859)(372,860)(373,862)(374,861)(375,864)
(376,863)(377,850)(378,849)(379,852)(380,851)(381,853)(382,854)(383,855)
(384,856)(385,873)(386,874)(387,875)(388,876)(389,878)(390,877)(391,880)
(392,879)(393,866)(394,865)(395,868)(396,867)(397,869)(398,870)(399,871)
(400,872)(401,889)(402,890)(403,891)(404,892)(405,894)(406,893)(407,896)
(408,895)(409,882)(410,881)(411,884)(412,883)(413,885)(414,886)(415,887)
(416,888)(417,905)(418,906)(419,907)(420,908)(421,910)(422,909)(423,912)
(424,911)(425,898)(426,897)(427,900)(428,899)(429,901)(430,902)(431,903)
(432,904)(433,921)(434,922)(435,923)(436,924)(437,926)(438,925)(439,928)
(440,927)(441,914)(442,913)(443,916)(444,915)(445,917)(446,918)(447,919)
(448,920)(449,937)(450,938)(451,939)(452,940)(453,942)(454,941)(455,944)
(456,943)(457,930)(458,929)(459,932)(460,931)(461,933)(462,934)(463,935)
(464,936)(465,953)(466,954)(467,955)(468,956)(469,958)(470,957)(471,960)
(472,959)(473,946)(474,945)(475,948)(476,947)(477,949)(478,950)(479,951)
(480,952);
poly := sub<Sym(960)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope